Entanglement from density measurements: Analytical density functional for the entanglement of strongly correlated fermions

Abstract

We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local-density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations-which includes reproducing subtle signatures of the particle density stages-shows that our density functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, in contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.

Entanglement enhancement in spatially inhomogeneous many-body systems

“…We find that only the impurity entanglement [case (i)] vanishes for V t, as the reduced density matrix of the impurity sites is pure in this limit (ρ x = ρ imp = |0 0|). For the average over all possible bipartitions [case (iii)], we find that the entanglement decreases with V , but saturates at a finite value, which is consistent with previous observations [12,[17][18][19]. Our results in Fig.…”

“…Either naturally occurring, as in disordered media, or artificially prepared in nanostructures and ultracold atoms, spatial inhomogeneity can influence optical, electrical, magnetic, transport, and entanglement properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Therefore, it is of great fundamental and technological interest.…”

“…The impact of spatial inhomogeneities on entanglement, which is a key ingredient in quantum information theory, has been investigated in spin chains, Kondo and Hubbard models [12][13][14][15][16][17][18][19]. The main goal is the development of solidstate devices for quantum information processing [14,20], for which accessing high degrees of entanglement, despite the inhomogeneities, is essential.…”

“…(2) below]. The influence of several types of inhomogeneities was analyzed: localized impurities and superlattice structures [17], harmonic traps [17][18][19], and disorder [12]. Although entanglement depends on the specific inhomogeneous component of the potential, the effect of inhomogeneities was, remarkably, found to be qualitatively the same in all cases: entanglement decreases.…”

Ab initiotheory of spin entanglement in atoms and molecules

“…There one needs to reconsider the definition of entanglement, by introducing suitable criteria for identifying the subsystems [3]. In the case of a many-electron system, for example, the subsystems can be identified with the lattice sites [4][5][6][7] or with a set of relevant orbitals [8][9][10][11], and their states are defined by the corresponding occupation numbers. Most of the potential applications can however be related to the so-called entanglement of particles [12,13], where each subsystem is associated to a definite number of particles (typically one).…”